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What is the probability researchers will reject their null hypothesis

What is the probability researchers will reject their null hypothesis

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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What is the probability researchers will reject their null hypothesis

estion 2 of 20 Attempt 14 Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample 50 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the supplement. Assume that the researchers know from prior experiments that the standard deviation of weight lost in one month, o, is 1.5 lb. To show that the supplement is effective, they plan to use a one-sample z-test of Ho: u = 0 lb against H:µ> 0 lb, where is the mean amount of weight lost in one month. They have also determined that, for a test with a significance level of 0.01, the power of the test is 0.8348 if the mean amount of weight lost is actually 0.7 lb. What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.7 lb or more? Give your answer as a percentage, precise to two decimal places. LEGO contact.us help pivecy policy terms.of use 5:14 PM about us Careers 12/4/2020 a : 23 2 |耳門
Transcribed Image Text:estion 2 of 20 Attempt 14 Suppose that a group of researchers is planning to test a new weight loss supplement. They have selected a random sample 50 people who are trying to lose weight and plan to measure the amount of weight lost after one month of using the supplement. Assume that the researchers know from prior experiments that the standard deviation of weight lost in one month, o, is 1.5 lb. To show that the supplement is effective, they plan to use a one-sample z-test of Ho: u = 0 lb against H:µ> 0 lb, where is the mean amount of weight lost in one month. They have also determined that, for a test with a significance level of 0.01, the power of the test is 0.8348 if the mean amount of weight lost is actually 0.7 lb. What is the probability that the researchers will reject their null hypothesis if the mean amount of weight lost is 0.7 lb or more? Give your answer as a percentage, precise to two decimal places. LEGO contact.us help pivecy policy terms.of use 5:14 PM about us Careers 12/4/2020 a : 23 2 |耳門
Expert Solution
Step 1

From the available information, 

Population mean, μ= 0.7

Population Standard deviation,σ = 1.5

Sample size, n= 50

The standard error is,

Se =σn=1.550=0.2121

The level of significance is,α = 0.01

From standard normal table at 0.01 level of significance the  right tailed critical value is,

zα=z(0.01) = +2.326

The power  of the test is denoted by 1-β.

Here β is the probability of making type 2 error.

That is fail to reject the null hypothesis .

Reject Ho if x¯-μ(σ/n)>zα

 

That is,

x¯ =μ+zα(σn)

 =  0+zα * Se

= 2.326* (0.2121)

 = 0.4933446

= 0.4934

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